1. ## Limits question

Determine the limit:

lim x→−3 √ (x^2 + 7 − 4)/(x^2 − 9)

So I'm pretty sure it doesn't exist but i just wanted to make sure... i got it down to

√(x^2+3)/(x+3)(x-3)

which doesn't exist because it equals zero

thanks for any help

Determine the limit:

lim x→−3 √ (x^2 + 7 − 4)/(x^2 − 9)

So I'm pretty sure it doesn't exist but i just wanted to make sure... i got it down to

√(x^2+3)/(x+3)(x-3)

which doesn't exist because it equals zero

thanks for any help
$\lim_{x\to{-3}}\frac{\sqrt{x^2+3}}{x^2-9}$

Multiplying by $\frac{\frac{1}{\sqrt{x^2}}}{\frac{1}{\sqrt{x^2}}}$

You will get the answer to be either infinity or undefined..whichever your instructor prefers

This is because

Determine the limit:

lim x→−3 √ (x^2 + 7 − 4)/(x^2 − 9)

So I'm pretty sure it doesn't exist but i just wanted to make sure... i got it down to

√(x^2+3)/(x+3)(x-3)

which doesn't exist because it equals zero

thanks for any help
For convenience, let f(x) = √(x^2+3)/(x+3)(x-3).

Note that $\lim_{x \rightarrow -3^+} f(x) = -\infty$ but $\lim_{x \rightarrow -3^-} f(x) = + \infty$.

The left hand limit does not equal the right hand limit.

Therefore $\lim_{x \rightarrow -3} f(x) = +\infty$ does not exist.